Continuously tunable optical dispersion compensation synthesizers using cascaded etalons

ABSTRACT

Described is a method for designing individual stages of a multiple cascaded etalon TDC device to allow continuous thermo-optic tuning over a desired range without inducing incremental signal distortion due to uncontrolled and unpredictable dispersion of the TDC during tuning. This allows the signal to transmit without encountering periods of incremental distortion or dark spots. The method includes prior knowledge of each etalon stage, after full assembly, for spectral group delay profile as a function of temperature through modeling and/or characterization. Characterization can account for performance variations that are due to allowed manufacturing tolerances.

RELATED APPLICATION

This application is a continuation of application Ser. No. 11/977,798,filed Oct. 26, 2007 now U.S. Pat. No. 7,706,045.

FIELD OF THE INVENTION

The field of the invention is optical dispersion compensation. Morespecifically, it is directed to methods for designing cascaded etalonsto produce tunable dispersion compensation synthesizers, and methods fortuning them.

BACKGROUND OF THE INVENTION

As optical systems migrate to higher transmission rates, such as 40 Gbs,there is a need to compensate for chromatic dispersion and to optimizeresidual chromatic dispersion in the system to minimize transmissionpenalty. Residual dispersion is an artifact of imperfect match betweenthe dispersion in the fiber plant and the fixed dispersion compensatorsused in typical optical transmission systems. To solve this problem,considerable effort has been devoted to the development of tunabledispersion compensation devices to replace and/or supplement existingfixed dispersion compensation devices. Moreover, as optical transmissionsystems evolve to more flexible and re-configurable systemarchitectures, there is a need to dynamically compensate for chromaticdispersion as node distances change through reconfiguration or as aresult of temperature changes.

To minimize transmission penalty due to chromatic dispersion at hightransmission bit rates such as 40 Gbps, close-loop tuning methods aretypically used. In the closed-loop method the feedback signal to thecontroller is correlated to system penalty and the controlled tuningdevice is a tunable dispersion compensator (TDC). Tuning dispersion in aclosed-loop system requires that the device tunes both dispersion anddispersion slope continuously over the complete dispersion range andacross all network channels. In available TDCs, as the dispersion istuned from one value to another, the signal may pass through timeperiods of unpredictable signal distortion due to uncontrolleddispersion of the TDC before arriving at the desired state. Currentlythere is no known solution which guarantees avoidance of these periodsof additional signal distortion between dispersion setpoints foretalon-based dispersion compensation devices.

There are a number of known approaches to provide tunable dispersioncompensation. Technologies includes: Etalons, Fiber-Bragg Gratings(FBG), Arrayed Waveguide Gratings (AWG), Virtual Imaged Phase Array(VIPA), Mach-Zehnder Interferometers (MZI), and Planar LightwaveCircuits (PLC). None of these technologies have produced satisfactorycontinuous dispersion tuning and/or continuous dispersion slope tuning.

STATEMENT OF THE INVENTION

We have developed a method for designing individual stages of a multiplecascaded etalon TDC device to allow methods for continuous thermo-optictuning over a desired range without inducing periods of incrementalsignal distortion between desired dispersion value setpoints. Thisallows the signal to be compensated without going through periods ofincremental impaired quality or dark spots during tuning. The methodinvolves prior knowledge of characterizing each etalon stage, after fullassembly, for spectral group delay profile as a function of a controlparameter such as temperature. This can be accomplished through modelingor characterization to account for performance variations that are dueto allowed manufacturing tolerances. The group delay profiles are thenfitted to an expected theoretical group delay profile based on theetalon structure design. Typical parameters varied to achieve the bestfit are: surface reflectivity, cavity free spectral range (FSR), and agroup delay offset and slope term to account for uncertainty in groupdelay measurements. The resulting theoretical etalon group delayprofiles of the individual stages are used in a series of solveralgorithms to identify etalon positions (temperatures) that bestsynthesize a target dispersion and, optionally, dispersion slope over atarget dispersion passband (channel width) and wavelength range (set ofchannels).

BRIEF DESCRIPTION OF THE DRAWING

The invention may be better understood when considered in conjunctionwith the drawing in which:

FIG. 1 is a schematic diagram illustrating the operation of a typicaletalon;

FIG. 2 is a schematic representation of a three stage cascaded TDC usingetalons with individual temperature controls;

FIG. 3 is a schematic representation of a dual-cavity etalon used inpreferred designs produced by the methods of the invention;

FIG. 4 is a plot of group delay in picoseconds vs. wavelength showingthe measured group delay profile for an individual etalon stage at threedifferent temperatures;

FIG. 5 is a graph representing the step of fitting the physical model ofthe group delay at a given temperature setting to the measured groupdelay at that temperature;

FIG. 6 is a chart of fit results from the Fabry-Pérot physical model;

FIG. 7 is a plot of individual group delay (left ordinate, multiplecurves) and the synthesized group delay (right ordinate, dark curve) vs.channel width in MHz showing the expanded channel produced by cascadingmultiple etalon stages;

FIG. 8 is a plot for 12 individual etalon stages showing dispersion vs.temperature;

FIG. 9 is a plot of dispersion vs. ITU wavelength for the 12 stages ofFIG. 8;

FIG. 10 is a plot of target dispersion vs. temperature set point givingen example of a 12 stage TDC device designed according to on aspect ofthe invention; and

FIG. 11 is a plot of average dispersion vs. wavelength illustratingdispersion slope compensation according to another aspect of theinvention.

DETAILED DESCRIPTION Of The INVENTION

The design methods of the invention are intended for any suitable etalonstructures. The preferred embodiments are Fabry-Pérot (FP) etalons,Gires-Tournoise (GT) etalons, and combinations thereof. The descriptionbelow focuses mainly on etalons and combinations of etalons that includeat least one FP etalon, although it should be understood that theinvention is not so limited.

A Fabry-Pérot etalon is typically made of a transparent plate with tworeflecting surfaces. An alternate design is composed of a pair oftransparent plates with a gap in between, with any pair of the platesurfaces forming two reflecting surfaces The transmission spectrum of aFabry-Pérot etalon as a function of wavelength exhibits peaks of largetransmission corresponding to resonances of the etalon. Referring toFIG. 1, light enters the etalon and undergoes multiple internalreflections. The varying transmission function is caused by interferencebetween the multiple reflections of light between the two reflectingsurfaces. Constructive interference occurs if the transmitted beams arein phase, and this corresponds to a high-transmission peak of theetalon. If the transmitted beams are out-of-phase, destructiveinterference occurs and this corresponds to a transmission minimum.Whether the multiply-reflected beams are in-phase or not depends on thewavelength (λ) of the light, the angle the light travels through theetalon (θ), the thickness of the etalon (l) and the refractive index ofthe material between the reflecting surfaces (n).

Maximum transmission (T_(e)=1) occurs when the optical path lengthdifference (2nl cos θ) between each transmitted beam is an integermultiple of the wavelength. In the absence of absorption, thereflectivity of the etalon R_(e) is the complement of the transmission,such that T_(e)+R_(e)=1, and this occurs when the path-length differenceis equal to half an odd multiple of the wavelength.

The finesse of the device can be tuned by varying the reflectivity ofthe surface(s) of the etalon. The finesse of the etalon is related tothe etalon reflectivities by:

$F = \frac{{\pi( {R_{1}R_{2}} )}^{1/4}}{1 - ( {R_{1}R_{2}} )^{1/2}}$where F is the finesse, R₁, R₂ are the reflectivity of facet 1 and facet2 of etalon. The GT etalon is essentially an FP etalon with one surfacehighly reflective.

The wavelength separation between adjacent transmission peaks is thefree spectral range (FSR) of the etalon, Δλ, and is given by:Δλ=λ₀ ²/2n/cos Θτwhere λ₀ is the central wavelength of the nearest transmission peak. TheFSR is related to the full-width half-maximum by the finesse of theetalon. Etalons with high finesse show sharper transmission peaks withlower minimum transmission coefficients.

The FSR of an etalon is temperature sensitive because the optical lengthof the etalon or the refractive index within the etalon is typicallytemperature sensitive. This temperature sensitivity, typically unwanted,can be used to advantage, if controlled, to tune a device thatincorporates an etalon. In a TDC, the dispersion of the device can bechanged by changing the temperature of the etalon. In a TDC with asingle etalon device, this tuning method may be relativelystraightforward. However, the tuning range and dispersion slopecapability is limited.

To increase the tuning range and improve the dispersion slope, multiplestages are used. In principle, a multiple cavity etalon, where basicallyseveral etalon plates are optically coupled together, could be used toincrease the dispersion tuning range or slope. However, in practice theetalons do not have the same group delay profile. That means that for aneffective TDC, the control parameter, such as temperature, of each stageshould be independently controlled. It also means that each stage shouldbe physically separate from other stages, sufficiently removed to allowthe temperature of the etalon(s) in each stage to be independentlycontrolled.

As mentioned above, obtaining a desired tuning result with a singlestage is straightforward, although a single stage TDC is of limitedinterest. But the problem becomes rapidly more complex as stages areadded to obtain a more broadly useful TDC. Tuning parameters in a one ortwo stage TDC may be related using an empirically based method. However,achieving useful compensation tuning in a TDC with three or more stagesrequires a new design approach.

FIG. 2 shows a TDC device with three stages. 21, 22, 23. The threestages are optically coupled by means (not shown) that connects thestages serially as indicated in the figure. Each of the three stagescomprises an etalon 24, 25, 26, and each is provided with an individualtemperature control 27, 28, 29. Two stages in the device is a practicalminimum for the methods described here. However, it is anticipated thatmost applications will employ at least three stages. Designing TDCdevices with more, and many more, stages is the objective of thesemethods. It is desirable for the TDC device to be tunable over a rangeof at least 50 picoseconds (ps) per nanometer (nm), and preferably atleast 200 ps/nm. For this result the number of stages, usingconventional etalons, would typically exceed 5. We have designed etalonswith even larger tuning ranges that use 12, 14, or 16 stages.

The design methods of primary interest here are for optical transmissionsystems that typically operate at and near 1.55 microns. This means thatthe materials used for the etalons should have a transparent windowaround 1.55 microns. However, the design methods are useful for otherwavelength regimes as well. The wavelength range desired for many systemapplications is 1.525 to 1.570 microns. That range is used fordemonstrating the methods of the invention.

The structure of the etalons is essentially conventional, eachcomprising a transparent plate with parallel boundaries. A variety ofmaterials may be used, with the choice dependent in part on the signalwavelength, as just indicated. The optical characteristics of etalonsvary with temperature due to at least two parameters. The variation ofrefractive index with temperature, commonly referred to as thethermo-optic effect, and written as dn/dt, which changes the opticalpath length between the optical interfaces, and the coefficient ofthermal expansion (CTE) which changes the physical spacing between theoptical interfaces. In standard etalon device design, the opticalsensitivity of the device to temperature changes is minimized. Materialsmay be chosen that have low dn/dt, and/or low CTE. Materials may also bechosen in which the dn/dt and the CTE are opposite in sign andcompensate. Common materials for etalons are fused quartz, tantalumpentoxide or niobium pentoxide. Semiconductor materials or glasses mayalso be used.

It is preferred that the design methods of this invention be based onsilicon as the bulk etalon substrate material. Silicon has a largethermo-optic coefficient and therefore is contra indicated for mostoptical devices. However, amorphous silicon, polysilicon, and preferablysingle crystal silicon, are recommended for the methods described herebecause a large thermo-optic coefficient is desirable. The thermo-opticcoefficient of single crystal silicon is approximately 1.9 to 2.4×10⁻⁴per degree K. over the temperature ranges used for tuning the etalons.

An embodiment of a TDC device for which the method of the invention isespecially suitably applied is shown in FIG. 3. In this embodiment atwin cavity etalon is used in each stage. The heating element (notshown) is adjacent to etalon 2, as suggested by FIG. 2. The preferredform of twin cavity etalon is a combination FP/GT etalon. In the FPcavity of the twin cavity etalon, both surfaces have a reflectivity<<100%, while in the GT cavity of the twin cavity etalon thereflectivity of one surface of the etalon is <<100% and the reflectivityof the other surface is near 100%. FIG. 3 shows the Fabry-Pérot cavityas etalon 1, and the GT cavity as etalon 2. Relevant parameters for thetwin cavity are T1, the thickness of the Fabry-Pérot etalon, T2, thethickness of the GT etalon, P1, the reflectivity of the input interfaceof the Fabry-Pérot etalon, P3, the reflectivity of the back face (highreflectivity face) of the GT etalon, and P2 the reflectivity of theinterface shared between the two cavities. The surface P1 is a lowreflectivity surface, P2 is a medium reflective surface and P3 is a highreflectivity surface. In general the reflectivity of P1 may vary over arange 0-25%, the reflectivity of P2 may vary over a range 35-80%, andthe reflectivity of P3 may vary over a range of 98-100%, preferably 99.5to 100%.

Typical dimensions for the etalons are 1.8 mm square, with the opticalwindow approximately 1.5 mm square. Thickness, T1 and T2, is typicallyapproximately 0.8 mm. Suitable reflectance values, with reference toFIG. 3, are shown in the following table.

Slicon Dual-Cavity Etalon Variant Table FSR P1 P2 P3 Mismatch PartNumber Reflectance Reflectance Reflectance (T1-T2) Class A Etalon  3.5 ±2% 40.5 ± 2% >99.95% 0-2/+3 MHz Class B Etalon  6.5 ± 2% 53.0 ±2% >99.95% 0-2/+3 MHz Class C Etalon 10.5 ± 2% 65.5 ± 2% >99.95% 0-1/+3MHZ Class D Etalon 15.0 ± 1% 74.0 ± 1% >99.95% 0-1/+2 MHz Class E Etalon19.0 ± 2% 79.5 ± 2% >99.95% 0-2/+3 MHz

The use of twin cavities as shown in FIG. 3, reduces the complexity ofthe tuning mechanism while still allowing the tuning range to beincreased. For the methods of the invention, prior knowledge, viamodeling and/or characterization, of each twin cavity stage is requiredin terms of the spectral group delay profile as if the twin cavityetalon is a single cavity etalon. However, the twin cavity etalon widensthe dispersion tuning range as if it were two stages. The embodiment ofFIG. 3 shows twin cavity etalons for reducing the tuning complexity ofthe device, more than two cavities may be optically coupled together forthe same purpose.

It will be evident to those skilled in the art that the tuning methodsdescribed here rely on changing the control parameter such astemperature of the etalon stages over a significant range, T2-T1. Thereis an inherent and unavoidable time delay, D=t2−t1, required to effectthe temperature change. This inherent delay D may be several seconds. Itis important to users of these devices what occurs during that timedelay. In most cases with thermally tuned TDC devices, and in all caseswith complex multi-stage thermo-optic tuning of TDC devices, the signalwill experience one or more periods of unpredictable distortion due touncontrolled dispersion of the TDC. It is not uncommon for the signal tosee excessive distortion momentarily as the device is tuned. The designmethod described in detail below has the capability of avoiding periodsof unpredictable distortion in the signal during tuning. It also has themore demanding objective of continuous tuning. Continuous dispersiontuning means that the signal at time t1 undergoes predictable andmonotonic change in dispersion through the delay period until it reachesthe final dispersion value at time t2.

The design method of the invention requires knowledge of the group delayof each stage which can be accomplished through one or more steps ofcharacterization after full assembly, for spectral group delay profileas a function of the control parameter such as temperature. Usingcharacterization accounts for performance variations that are due toallowed manufacturing tolerances. The group delay profiles are thenfitted to an expected theoretical group delay profile based onplane-wave matrix modeling of coupled interferometers. Typicalparameters varied to achieve the best fit are: surface 1 and 2reflectivity, cavity 1 and 2 free spectral range (FSR), and a groupdelay offset and slope term to account for uncertainty in group delaymeasurements. The resulting theoretical etalon group delay profiles ofthe individual stages are used in a series of solver algorithms toidentify etalon positions (temperatures) that best synthesize a targetdispersion and dispersion slope over a target dispersion passband(channel width) and wavelength range (set of channels). Constraints inthe solver algorithm include the etalon temperature range, and therequirement to avoid significant discontinuities over dispersion range.The solver repeats this process over the range of target dispersions tofind discrete solutions at ‘coarse’ dispersion increments (e.g. 10-200ps/nm) to create a complete etalon mapping of temperature versusdispersion using previous solution as a start point. This mapping isthen used by the embedded controls to set the etalon temperatures forany desired dispersion within the stated range. The constraints used aspart of the solver algorithms provide a mapping that is continuous suchthat the discrete solutions, obtained at ‘coarse’ dispersion increments(e.g. 10-200 ps/nm), can be used by the controller to set any ‘fine’dispersion increment (<1 ps/nm) by interpolating the ‘coarse’ positionsto solve for etalon temperatures. This results in a device that meetsdispersion accuracy, and group delay ripple performance, continuouslyover the dispersion set points in the stated range of dispersion.

FIGS. 4-7 illustrate typical parameters used for designing TDCsynthesizers according to the methods of the invention. An example ofthe methods is described below in conjunction with these figures.

Step 1. Characterize Each Individual Stage by Measured Group Delay orPhase.

-   -   With reference to FIG. 4, each individual stage is characterized        by measured Group Delay (or Phase) as a function of wavelength        and temperature over one or more FSR's within ranges of        operating channel(s), wavelength and temperature. This step        follows a recognition that fabricating etalons for precision        thermo-optically tuned TDC devices according to demanding        manufacturing specifications is generally not sufficient to        obtain the result desired here, namely continuous tuning between        dispersion compensation values. As indicated previously,        continuous tuning between dispersion compensation values means        that the signal quality undergoes continuous improvement during        tuning. To achieve this, it has been found useful to        individually characterize each etalon stage as a preliminary to        the design of cascaded stages. This step produces a desired        group delay function using multiple concatenated group delay        stages. Characterization is done at multiple wavelength        channels, multiple temperatures, and in fine enough increments        to account for any nonlinearities in the group delay response as        a function of wavelength channel and temperature. FIG. 4 is a        plot of the group delay vs. wavelength at three different        temperatures. 40 C., 75 C., and 115 C. Characterization includes        measurement data and/or predictive data.

Step 2. Fit Group Delay Measured Responses Using an Etalon BasedPhysical Model.

-   -   With reference to FIG. 5, the measured group delay responses are        fit to the etalon based physical model with variables being        surface reflectance, cavity FSR/thickness, and temperature        coefficients. FIG. 5 shows data for several individual etalon        stages (multiple shades of curves related to left ordinate) and        the group delay curve (heavy black line related to right        ordinate). Fitting the data to match a physical etalon model        will produce an accurate mathematical representation/model of        the device response that can easily be computed at any        frequency. Variations in surface reflectances and cavity        FSR/thickness and temperature coefficients that occur in        manufacture are accounted for to ensure that the model        accurately represents the actual device.

Step 3. Solve Each Individual Stage Fabry-Pérot Plane-Wave Matrix ModelParameters as a Function of Temperature.

-   -   Achieving a desired overall concatenated group delay requires        knowledge of the individual stage group delay response as a        function of temperature because temperature is the control        parameter used to position each stage. Manufacturing variations,        including surface reflectances, cavity FSR/thickness, and        temperature coefficients, will be accounted for to enable the        model to accurately represent the actual device at any        temperature over the expected temperature tuning range. Prior to        fitting, group delay measurements should be done in adequate        temperature increments to quantify and model any non-linearities        in group delay response.

Step 4. Provide Dispersion Synthesizer Inputs

-   -   The dispersion synthesizer is the mathematical engine that        adjusts the temperatures of individual etalon stages (the        outputs from the physical model) to produce a desired        concatenated dispersion and/or group delay response. Inputs to        the synthesizer include: desired group delay and/or dispersion        response over one or more ITU channel, bandwidth over which the        response is required, Figure of Merit to optimize the        temperature ranges of the individual etalon stages, and the        physical model of the etalon stages. The synthesizer uses one or        more optimization algorithms to find a combination of etalon        temperatures that produce an acceptable result. Optimization        models include genetic and gradient-based classifications of        models. A genetic algorithm is used for initial partial solution        at a maximum or minimum dispersion, then gradient-based        algorithm uses the genetic partial solution and refines it. This        multiple model approach optimizes efficiency and probability of        achieving a global solution.

Step 5. Define the Figure of Merit

-   -   The metric used for the optimization is a figure of merit which        quantifies how well the simulated response meets the        requirements of the desired response. (The desired response may        be group delay or dispersion.) A suitable figure of merit can be        defined by: best fit to a target dispersion, best fit to a        target group delay, etc. A tolerance value is specified and used        to tell the optimizer when it has found an acceptable solution.

Step 6. Solve for Individual Etalon Stage Temperatures for the Minimumand Maximum Desired Dispersion Target(s).

-   -   Because the device is tunable, more than one desired dispersion        or group delay response and the optimization begins with a        single target. Since there are multiple solutions for any given        target and the solutions are not independent (to satisfy        continuity), an optimizer algorithm is more effective with        finely spaced and ordered targets. The resulting data may be        used in a plot such as that shown in FIG. 7. FIG. 7 plots the        desired dispersion setpoint vs. the etalon temperature for a 12        stage TDC device. As is evident, to achieve the desired TDC        tuning range, four of the stages undergo very significant        temperature excursions, i.e. about 35 degrees C.

Step 7. Iteratively solve individual etalon stage temperatures for eachdispersion/group delay target(s) at a finite dispersion interval in asystematic and continuous fashion. Since the device tunes continuouslyfrom one target to another, the solutions for the individual targetsshould be continuous. Continuous solutions are defined by the relativebehavior of each stage temperature as it tunes from one target toanother. To be continuous, each stage temperature should movemonotonically (or very near monotonically) as the device is tuned overthe range of dispersion or group delay targets. If each stage ismonotonic, the resulting dispersion or group delay response of thedevice between two targets (during transition) will lie within the rangeof the two targets, i.e. not lower than either target or higher thaneither target. The interval at which the solutions are determinedthrough optimization should be adequate to guarantee that targets withinthe interval are valid and the device will achieve the expected responseperformance at the expected intervals.

Step 8. Create a Dispersion Map from the Optimization Outputs.

-   -   When the optimizations are complete, a 2-dimensional array of        dispersion or group delay target versus stage etalon temperature        is generated and used for setting dispersion/group delay        targets. This data can be downloaded to the device controller        for setting and controlling dispersion/group delay setpoints. A        typical dispersion map is shown in FIG. 8, where dispersion is        plotted as the ordinate vs. wavelength as the abscissa.

Step 9. Estimate Individual Etalon Stage Temperatures for any DesiredDispersion/Group Delay within a Range in the Dispersion Map UsingAppropriate Interpolation Model.

-   -   Since the method described above produces a series of continuous        dispersion solutions for the individual etalon stage        temperatures, the device can operate at dispersion targets that        lie between any 2 adjacent solutions. To estimate the individual        etalon stage temperatures for dispersion/group delay targets        that lie between 2 adjacent solutions, a simple interpolation of        each of the etalon stage temperatures between those same 2        adjacent solutions can be used.

Whereas the foregoing description deals mainly with devices used fordispersion compensation it will be evident to those skilled in the artthat the devices described are capable of tuning dispersion values forother applications.

Those skilled in the art will appreciate that in situations describedabove wherein the signal is described as “hitless” while the device istuned means that the TDC is in use during tuning, i.e., an opticalsignal is being transmitted through the WDM system that incorporates theTDC. It should also be evident that the TDC can be tuned while thesystem is not in service, i.e. when there is no optical signal throughthe TDC device. However, in most cases dynamic tuning will be employed,and the signal quality can be observed as the TDC is tuned. In somecases, an optical test signal may be employed.

It should be evident that the method just described can be fullyautomated to provide continuous dispersion compensation for the opticalsystem. When a dispersion drift is detected, the system willautomatically compensate for the drift as soon as it is detected.However, in many cases the system dispersion change is not a drift butan incremental change, sometimes a large incremental change. This mayhappen if the system is reconfigured for new or repaired services. Thusthe TDC may be required to compensate over large dispersion values, andthus make large temperature excursions.

Various additional modifications of this invention will occur to thoseskilled in the art. All deviations from the specific teachings of thisspecification that basically rely on the principles and theirequivalents through which the art has been advanced are properlyconsidered within the scope of the invention as described and claimed.

1. A method for tuning a multistage etalon tunable dispersioncompensator having at least two etalon stages, the method comprising thesteps of: characterizing a group delay profile for each of the etalonstages as a function of wavelength and temperature based on actualmeasurements of group delays of the etalon stages over a range ofwavelengths and temperatures, wherein each characterized group delayprofile is based on the actual measurements to account for variations insurface reflectance, cavity free spectral range, and temperaturecoefficient of the corresponding etalon stage; determining a targetcontrol parameter for each of the etalon stages based on thecharacterized group delay profiles and a target dispersion value; andcontrolling each of the etalon stages according to the target controlparameter thereof.
 2. The method of claim 1, wherein the target controlparameter for each of the etalon stages is a cavity free spectral range(FSR) thereof.
 3. The method of claim 2, wherein a temperature of eachof the etalon stages is controlled to achieve the target FSR.
 4. Themethod of claim 3, wherein the temperature of each of the etalon stagesis controlled using a heating device attached thereto.
 5. The method ofclaim 1, wherein the target control parameters of the etalon stages arecontrolled to change a resulting dispersion value in a continuous andmonotonic manner.
 6. A tunable dispersion compensator comprising: two ormore etalon stages connected in a cascasded manner, each etalon stageconfigured with a heating device that is controlled to change atemperature of the etalon stage to a target temperature, wherein thetarget temperature for each of the etalon stages is set bycharacterizing a group delay profile of the etalon stage as a functionof wavelength and temperature based on actual measurements of groupdelays of the etalon stage over a range of wavelengths and temperatures,wherein each characterized group delay profile is based on the actualmeasurements to account for variations in surface reflectance, cavityfree spectral range, and temperature coefficient of the correspondingetalon stage, and determining the target temperature based on thecharacterized group delay profile of the etalon stage and a targetdispersion value, and the etalon stages are controlled to the targettemperatures to change a resulting dispersion value in a continuous andmonotonic manner.
 7. The tunable dispersion compensator of claim 6,wherein at least three etalon stages are connected in a cascasdedmanner.
 8. The tunable dispersion compensator of claim 6, wherein eachetalon stage includes an etalon made of silicon.
 9. The tunabledispersion compensator of claim 8, wherein the etalon includes aFabry-Perot etalon.
 10. The tunable dispersion compensator of claim 8,wherein the etalon includes a Gires-Tournois etalon.
 11. The tunabledispersion compensator of claim 6, wherein each etalon stage includes adual cavity etalon including a Fabry-Perot etalon and a Gires-Tournoisetalon.